Prime labeling is the most interesting category of graph labeling with various applications. A graph <em>G= (V(G), E(G))</em> with |<em>v(G)</em>| vertices are said to have prime labeling if its vertices are labeled with distinct positive integers 1,2,3,……,|<em>v</em>| such that for each edge <em>uv </em><em>e E(G)</em> the labels assigned to <em>u</em> and <em>v</em> are relatively prime, where <em>V(G)</em> and <em>E(G) </em>are vertex set and edge set of <em>G</em>, respectively. Therefore, the graph <em>G</em> has a prime labeling whenever any of two adjacent vertices can be labeled as two relative prime numbers and is called a prime graph. In our work, we focus on the prime labeling method for newly constructed graphs obtained by replacing each edge of a star graph <em>K</em><sub>1<em>,n</em> </sub>by a complete tripartite graph <em>K</em><sub>1<em>,m,</em>1</sub> for <em>m</em> = 2,3,4, and 5, which are prime graphs. In addition to that, investigate another type of simple undirected finite graphs generalized by using circular ladder graphs. These new graphs obtained by attaching <em>K</em><sub>1,2 </sub>at each external vertex of the circular ladder graph <em>CL<sub>n</sub></em> and proved that the constructed graphs are prime graphs when <em>n </em>≥ 3 and <em>n </em><em>≠</em> 1 (<em>mod3</em>) . Finally, focus on another particular type of simple undirected finite graph called a scorpion graph, denoted by <em>S</em>(2<em>p</em>,2<em>q</em>,<em>r</em>) . The Scorpion graph gets its name from shape, which resembles a scorpion, having 2<em>p</em> + 2<em>q</em> + <em>r</em> vertices <em>p</em> ≥ 1, <em>q </em>≥ 2, <em>r</em> ≥ 2)are placed in the head, body, and tail respectively. To prove that the scorpion graph has prime labeling, we used two results that have already been proved for ladder graphs.